My daughter is 15 weeks old If her father and I were to go to court what are the visitation rights for a infant under the age of one? He is a good father but I am the primary care giver he doesn't know what any of her cries mean, how to give her a bath or when to feed her.I just really want to know if there is any special visitation laws for a baby that young.

Generally there's no overnight visitation for a child that young. That is the only "special" visitation "law" (more accurately, precedent) that I am aware of.

First have you even gotten custody order yet. That is the first issue, and I will disagree I have seen where fathers get joint custody if they have filed for it, as well as standard visiation.

Assuming you two are not or was not married the visitation has to be supervised meaning you there at all times or someone you trust, family member or whatever, until the child reaches 5yrs. Then the father could take you back to court for more rights including unsupervised, overnights, weekends and such.
They usually give fathers 2-3hrs 1 day a week visitation.
No guaranties on this but this was my experience in this situation. It probably varies from state to state though.
If you two are married that is a different story. Then he could get shared custody or weekends.